A244185 T(n,k)=Number of length n+4 0..k arrays with no five consecutive elements with pattern ababa or abbba (possibly a=b) and new values 0..k introduced in 0..k order

13, 38, 22, 48, 108, 36, 49, 173, 306, 59, 49, 188, 650, 867, 97, 49, 189, 790, 2495, 2457, 160, 49, 189, 811, 3537, 9667, 6963, 263, 49, 189, 812, 3803, 16477, 37604, 19732, 433, 49, 189, 812, 3831, 19113, 78614, 146521, 55918, 712, 49, 189, 812, 3832, 19575

Offset

1,1

Comments

Table starts

...13.....38......48.......49........49........49........49........49........49

...22....108.....173......188.......189.......189.......189.......189.......189

...36....306.....650......790.......811.......812.......812.......812.......812

...59....867....2495.....3537......3803......3831......3832......3832......3832

...97...2457....9667....16477.....19113.....19575.....19611.....19612.....19612

..160...6963...37604....78614....101200....107068....107818....107863....107864

..263..19732..146521...380407....556443....620051....631917....633072....633127

..433..55918..571315..1855983...3141344...3761768...3920234...3942493...3944198

..712.158464.2228340..9098538..18055451..23672967..25559691..25918400..25957707

.1172.449066.8692454.44726540.105031051.153195068.173884143.178997028.179748699

Links

R. H. Hardin, Table of n, a(n) for n = 1..4239

Formula

Empirical for column k:

k=1: a(n) = a(n-2) +a(n-3) +2*a(n-4) +a(n-5) +a(n-6)

k=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +5*a(n-4) +3*a(n-5) +2*a(n-6)

k=3: [order 12]

k=4: [order 18]

k=5: [order 24]

k=6: [order 30]

k=7: [order 36]

k=8: [order 42]

k=9: [order 48]

Example

Some solutions for n=6 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....0....1....1....1....0....1....1....1....1....1....1....1....1
..1....1....2....1....2....2....1....1....2....2....2....1....1....0....0....2
..0....2....3....2....0....3....2....2....1....3....0....2....2....2....0....2
..2....2....4....1....3....0....2....3....3....0....2....2....3....2....1....0
..3....1....4....2....0....1....3....3....3....0....3....0....4....3....0....3
..0....0....3....0....0....3....2....4....4....0....2....3....3....0....2....1
..0....0....2....0....4....4....1....4....0....4....1....0....3....1....3....4
..2....0....2....1....3....4....4....2....2....2....2....1....1....3....1....1
..3....0....0....2....0....1....0....1....1....0....4....1....1....4....1....2

Crossrefs

Column 1 is A164441(n+3)

Sequence in context: A201809 A129541 A302858 * A044090 A044471 A285525

Adjacent sequences: A244182 A244183 A244184 * A244186 A244187 A244188

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 21 2014

Status

approved